PCI Speed

i don't belive removing your modem or any other pci card would help, and as far as i know each pci slot is dsignated like usb. you wouldn't really speed up your video card. what is the brand and wattage of your psu? the onlt problem you could potentally have is voltage and that wouldnt nessicarily speed up or slow down your video card. i would leave every pci card in that is in. last question do you have a microATX board or standard board(how many pci slots do you have total??)

PCI is a bus, and all devices are connected to each other. If you are actively using the modem device, then yes, it will consume some (very little really) CPU power and bus bandwidth. It is easier to just hang up rather than remove the thing though

If you are overclocking in a way that actually increases the PCI clock speed, then removing less tolerant devices may let you go a bit further.

If you have a crappy sound card (integrated), then this will eat a lot of CPU power and precious PCI cycles when gaming.